This is a "spring-mass" mass problem.
g=32.2 ft/sec² (accel. due to gravity)
Let y=displacement (downwards) in the same direction as g, then the differential equation that governs the motion is:
acceleration = -ky, or
y"+ky=0 where y"=d²y/dt²
The solution of the auxiliary equation is
(m^2+k)=0, or m=±i√k
and the solution to the equation is
y=C1 cos(√k t) + C2 sin(√k t)
The initial conditions are:
y(0)=-0.5=C1 cos(0) + C2 sin(0)
C2=0, and C1=-0.5
y'(t)=-C2√k sin(√k t) + C2 √k cos(√k t)
y'(0)=0=-C2√k sin(0) + C2 √k cos(0)
C2=0 since sin(0)=0, √k≠0 and cos(0)≠0.
So the equation of motion is:
Answers to (b) and (c) can be deduced from the equation of motion.
math - a steel ball weighing 128 lb is suspended from a spring, whereupon the ...
Math Surveying - Hey, I need help working these problems. Thanks you. 1) A 50-m ...
critical thinking - A company can either invest in employee training seminars or...
IT 205 - outline the development of a high-level computer network design for the...
Physics - How do i get the answer A steel ball of diameter Lb = 4.196 cm is ...
solid mensuration - the area of the total surface of a polyhedron weighing 64 lb...
physics - 1) Two people sit on a park bench 6.0 ft long, weighing 160 lb. A boy ...
physics - Determine the moment of inertia for three children weighing 57.0 lb, ...
math help - Pat recorded the weights of the first ten fish she caught and ...
physics - a crane drops a .3 kg steel ball onto a steel plate. the ball's speeds...